Divisibility Rule for 3

Problem

Testing if large numbers are divisible by 3 requires actual division.

Solution

Sum all digits. If the sum is divisible by 3, the number is divisible by 3.

Benefit

Instant divisibility test without performing division.

Example

Is 2,847 divisible by 3?
2 + 8 + 4 + 7 = 21
21 ÷ 3 = 7 ✓
Yes, 2847 is divisible by 3

Is 5,923 divisible by 3?
5 + 9 + 2 + 3 = 19
19 is not divisible by 3 ✗